Most of the research in topological photonic structures has primarily been focused on the investigation of the linear optical response of such photonic systems. However, key functionalities of active photonic devices, such as tunability, optical frequency generation, and sensing, can most effectively be implemented by employing the nonlinear optical response of the underlying materials [1]}.To this end, active topological photonic devices relying on nonlinear optical effects, including Kerr effect [2]}, second-harmonic generation (SHG) [3]}, [4]}, third-harmonic generation (THG) [4]}, [6]}, [7]}, and four-wave mixing (FWM) [8]}, have been successfully demonstrated. In particular, frequency-mixing processes between phase-matched topological edge modes, including SHG [3]}, [4]}, [11]}, FWM [8]} and THG [4]}, [11]}, [7]}, have been recently studied in PhCs and two-dimensional (2D) materials. In addition, applications of these nonlinear optical effects to imaging of topological edge states via THG [6]}, lattice edge solitons [17]}, [18]}, traveling-wave amplifiers [19]}, topological sources of quantum light [20]}, and topological insulator lasers [21]}, [22]} have been proposed theoretically and in some cases demonstrated experimentally.
